Examples of EigenvalueDecomposition

Jama.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
cern.colt.matrix.linalg.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix A.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.mult(D.mult(transpose(V))) and V.mult(transpose(V)) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.mult(V) equals V.mult(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon Algebra.cond(V).
de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.timesTranspose(V)) and V.timesTranspose(V) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond(). @apiviz.uses Matrix - - transforms
org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition
@deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition
nist.gov/javanumerics/jama/
stallone.algebra.EigenvalueDecomposition
Data container for eigenvalue decomposition of a matrix @author noe
weka.core.matrix.EigenvalueDecomposition
nist.gov/javanumerics/jama/" target="_blank">JAMA package. @author The Mathworks and NIST @author Fracpete (fracpete at waikato dot ac dot nz) @version $Revision: 1.4 $

Examples of org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition

        {0,1,0,0},
        {0,0,1,0},
        {0,0,0,1} };
    Matrix matrix1 = new Matrix(m1);
      
    EigenvalueDecomposition e = new EigenvalueDecomposition(matrix1);
    
    double[] d1 = e.getImagEigenvalues();
    double[] d2 = e.getRealEigenvalues();
    Matrix mx = e.getV();
    
    Assert.assertEquals(1.0, mx.get(0,0));
    Assert.assertEquals(1.0, mx.get(1,1));
    Assert.assertEquals(1.0, mx.get(2,2));
    Assert.assertEquals(4, mx.getRows());

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Examples of org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition

        {0,1,0,0},
        {0,0,1,0},
        {1,0,0,1} };
    Matrix matrix1 = new Matrix(m1);
      
    EigenvalueDecomposition e = new EigenvalueDecomposition(matrix1);
    
    double[] d1 = e.getImagEigenvalues();
    double[] d2 = e.getRealEigenvalues();
    Matrix mx = e.getV();
    
    Assert.assertEquals(0.0, mx.get(0,0));
    Assert.assertEquals(0.0, mx.get(1,1));
    Assert.assertEquals(1.0, mx.get(2,2));
    Assert.assertEquals(4, mx.getRows());

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Examples of stallone.algebra.EigenvalueDecomposition

                info, tol, iparam, ipntr, ido);


        postprocess(n, bmat, which, ncv, resid, workd, lworkl, workl, v, info,
                tol, iparam, ipntr);


        result = new EigenvalueDecomposition(null, eigenvalues, rightEigenvectors);
    }

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Examples of weka.core.matrix.EigenvalueDecomposition

   * 
   * @param m    the matrix to determine the dominant eigenvector for
   * @return    the dominant eigenvector
   */
  protected Matrix getDominantEigenVector(Matrix m) {
    EigenvalueDecomposition  eigendecomp;
    double[]      eigenvalues;
    int        index;
    Matrix      result;
    
    eigendecomp = m.eig();
    eigenvalues = eigendecomp.getRealEigenvalues();
    index       = Utils.maxIndex(eigenvalues);
    result  = columnAsVector(eigendecomp.getV(), index);
    
    return result;
  }

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Examples of weka.core.matrix.EigenvalueDecomposition

    int        j;
    Vector<Integer>     deleteCols;
    int[]       todelete;
    double[][]       v;
    Matrix       corr;
    EigenvalueDecomposition   eig;
    Matrix       V;
    
    m_TrainInstances = new Instances(instances);


    // make a copy of the training data so that we can get the class
    // column to append to the transformed data (if necessary)
    m_TrainCopy = new Instances(m_TrainInstances, 0);


    m_ReplaceMissingFilter = new ReplaceMissingValues();
    m_ReplaceMissingFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_ReplaceMissingFilter);


    m_NominalToBinaryFilter = new NominalToBinary();
    m_NominalToBinaryFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_NominalToBinaryFilter);


    // delete any attributes with only one distinct value or are all missing
    deleteCols = new Vector<Integer>();
    for (i = 0; i < m_TrainInstances.numAttributes(); i++) {
      if (m_TrainInstances.numDistinctValues(i) <= 1)
  deleteCols.addElement(i);
    }


    if (m_TrainInstances.classIndex() >=0) {
      // get rid of the class column
      m_HasClass = true;
      m_ClassIndex = m_TrainInstances.classIndex();
      deleteCols.addElement(new Integer(m_ClassIndex));
    }


    // remove columns from the data if necessary
    if (deleteCols.size() > 0) {
      m_AttributeFilter = new Remove();
      todelete = new int [deleteCols.size()];
      for (i = 0; i < deleteCols.size(); i++)
  todelete[i] = ((Integer)(deleteCols.elementAt(i))).intValue();
      m_AttributeFilter.setAttributeIndicesArray(todelete);
      m_AttributeFilter.setInvertSelection(false);
      m_AttributeFilter.setInputFormat(m_TrainInstances);
      m_TrainInstances = Filter.useFilter(m_TrainInstances, m_AttributeFilter);
    }


    // can evaluator handle the processed data ? e.g., enough attributes?
    getCapabilities().testWithFail(m_TrainInstances);


    m_NumInstances = m_TrainInstances.numInstances();
    m_NumAttribs   = m_TrainInstances.numAttributes();


    //fillCorrelation();
    fillCovariance();


    // get eigen vectors/values
    corr = new Matrix(m_Correlation);
    eig  = corr.eig();
    V    = eig.getV();
    v    = new double[m_NumAttribs][m_NumAttribs];
    for (i = 0; i < v.length; i++) {
      for (j = 0; j < v[0].length; j++)
        v[i][j] = V.get(i, j);
    }
    m_Eigenvectors = (double[][]) v.clone();
    m_Eigenvalues  = (double[]) eig.getRealEigenvalues().clone();


    // any eigenvalues less than 0 are not worth anything --- change to 0
    for (i = 0; i < m_Eigenvalues.length; i++) {
      if (m_Eigenvalues[i] < 0)
  m_Eigenvalues[i] = 0.0;

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Examples of weka.core.matrix.EigenvalueDecomposition

    int        j;
    Vector<Integer>     deleteCols;
    int[]       todelete;
    double[][]       v;
    Matrix       corr;
    EigenvalueDecomposition   eig;
    Matrix       V;
    
    m_TrainInstances = new Instances(instances);


    // make a copy of the training data so that we can get the class
    // column to append to the transformed data (if necessary)
    m_TrainCopy = new Instances(m_TrainInstances);


    m_ReplaceMissingFilter = new ReplaceMissingValues();
    m_ReplaceMissingFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_ReplaceMissingFilter);


    if (m_Normalize) {
      m_NormalizeFilter = new Normalize();
      m_NormalizeFilter.setInputFormat(m_TrainInstances);
      m_TrainInstances = Filter.useFilter(m_TrainInstances, m_NormalizeFilter);
    }


    m_NominalToBinaryFilter = new NominalToBinary();
    m_NominalToBinaryFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_NominalToBinaryFilter);


    // delete any attributes with only one distinct value or are all missing
    deleteCols = new Vector<Integer>();
    for (i = 0; i < m_TrainInstances.numAttributes(); i++) {
      if (m_TrainInstances.numDistinctValues(i) <= 1)
  deleteCols.addElement(i);
    }


    if (m_TrainInstances.classIndex() >=0) {
      // get rid of the class column
      m_HasClass = true;
      m_ClassIndex = m_TrainInstances.classIndex();
      deleteCols.addElement(new Integer(m_ClassIndex));
    }


    // remove columns from the data if necessary
    if (deleteCols.size() > 0) {
      m_AttributeFilter = new Remove();
      todelete = new int [deleteCols.size()];
      for (i = 0; i < deleteCols.size(); i++)
  todelete[i] = ((Integer)(deleteCols.elementAt(i))).intValue();
      m_AttributeFilter.setAttributeIndicesArray(todelete);
      m_AttributeFilter.setInvertSelection(false);
      m_AttributeFilter.setInputFormat(m_TrainInstances);
      m_TrainInstances = Filter.useFilter(m_TrainInstances, m_AttributeFilter);
    }


    // can evaluator handle the processed data ? e.g., enough attributes?
    getCapabilities().testWithFail(m_TrainInstances);


    m_NumInstances = m_TrainInstances.numInstances();
    m_NumAttribs   = m_TrainInstances.numAttributes();


    fillCorrelation();


    // get eigen vectors/values
    corr = new Matrix(m_Correlation);
    eig  = corr.eig();
    V    = eig.getV();
    v    = new double[m_NumAttribs][m_NumAttribs];
    for (i = 0; i < v.length; i++) {
      for (j = 0; j < v[0].length; j++)
        v[i][j] = V.get(i, j);
    }
    m_Eigenvectors = (double[][]) v.clone();
    m_Eigenvalues  = (double[]) eig.getRealEigenvalues().clone();


    // any eigenvalues less than 0 are not worth anything --- change to 0
    for (i = 0; i < m_Eigenvalues.length; i++) {
      if (m_Eigenvalues[i] < 0)
  m_Eigenvalues[i] = 0.0;

View Full Code Here

Examples of weka.core.matrix.EigenvalueDecomposition

   * 
   * @param m    the matrix to determine the dominant eigenvector for
   * @return    the dominant eigenvector
   */
  protected Matrix getDominantEigenVector(Matrix m) {
    EigenvalueDecomposition  eigendecomp;
    double[]      eigenvalues;
    int        index;
    Matrix      result;
    
    eigendecomp = m.eig();
    eigenvalues = eigendecomp.getRealEigenvalues();
    index       = Utils.maxIndex(eigenvalues);
    result  = columnAsVector(eigendecomp.getV(), index);
    
    return result;
  }

View Full Code Here

Examples of weka.core.matrix.EigenvalueDecomposition

    int        j;
    Vector<Integer>     deleteCols;
    int[]       todelete;
    double[][]       v;
    Matrix       corr;
    EigenvalueDecomposition   eig;
    Matrix       V;
    
    m_TrainInstances = new Instances(instances);


    // make a copy of the training data so that we can get the class
    // column to append to the transformed data (if necessary)
    m_TrainCopy = new Instances(m_TrainInstances, 0);


    m_ReplaceMissingFilter = new ReplaceMissingValues();
    m_ReplaceMissingFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_ReplaceMissingFilter);


    m_NominalToBinaryFilter = new NominalToBinary();
    m_NominalToBinaryFilter.setInputFormat(m_TrainInstances);
    m_TrainInstances = Filter.useFilter(m_TrainInstances, m_NominalToBinaryFilter);


    // delete any attributes with only one distinct value or are all missing
    deleteCols = new Vector<Integer>();
    for (i = 0; i < m_TrainInstances.numAttributes(); i++) {
      if (m_TrainInstances.numDistinctValues(i) <= 1)
  deleteCols.addElement(i);
    }


    if (m_TrainInstances.classIndex() >=0) {
      // get rid of the class column
      m_HasClass = true;
      m_ClassIndex = m_TrainInstances.classIndex();
      deleteCols.addElement(new Integer(m_ClassIndex));
    }


    // remove columns from the data if necessary
    if (deleteCols.size() > 0) {
      m_AttributeFilter = new Remove();
      todelete = new int [deleteCols.size()];
      for (i = 0; i < deleteCols.size(); i++)
  todelete[i] = ((Integer)(deleteCols.elementAt(i))).intValue();
      m_AttributeFilter.setAttributeIndicesArray(todelete);
      m_AttributeFilter.setInvertSelection(false);
      m_AttributeFilter.setInputFormat(m_TrainInstances);
      m_TrainInstances = Filter.useFilter(m_TrainInstances, m_AttributeFilter);
    }


    // can evaluator handle the processed data ? e.g., enough attributes?
    getCapabilities().testWithFail(m_TrainInstances);


    m_NumInstances = m_TrainInstances.numInstances();
    m_NumAttribs   = m_TrainInstances.numAttributes();


    //fillCorrelation();
    fillCovariance();


    // get eigen vectors/values
    corr = new Matrix(m_Correlation);
    eig  = corr.eig();
    V    = eig.getV();
    v    = new double[m_NumAttribs][m_NumAttribs];
    for (i = 0; i < v.length; i++) {
      for (j = 0; j < v[0].length; j++)
        v[i][j] = V.get(i, j);
    }
    m_Eigenvectors = (double[][]) v.clone();
    m_Eigenvalues  = (double[]) eig.getRealEigenvalues().clone();


    // any eigenvalues less than 0 are not worth anything --- change to 0
    for (i = 0; i < m_Eigenvalues.length; i++) {
      if (m_Eigenvalues[i] < 0)
  m_Eigenvalues[i] = 0.0;

View Full Code Here

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